The present disclosure relates to systems and methods for magnetic resonance imaging (“MRI”). More particularly, the present disclosure relates to systems and methods for reconstructing images from data acquired with an MRI system.
Magnetic resonance imaging (“MRI”) uses the nuclear magnetic resonance (“NMR”) phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclei in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped,” into the x-y plane to produce a net transverse magnetic moment Mxy. A signal is emitted by the excited nuclei or “spins,” after the excitation signal B1 is terminated, and this signal may be received and processed to form an image.
When utilizing these “MR” signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The MR signals acquired with an MRI system are signal samples of the subject of the examination in Fourier space, or what is often referred to in the art as “k-space.” Each MR measurement cycle, or pulse sequence, typically samples a portion of k-space along a sampling trajectory characteristic of that pulse sequence. Most pulse sequences sample k-space in a raster scan-like pattern sometimes referred to as a “spin-warp,” a “Fourier,” a “rectilinear,” or a “Cartesian” scan. There are many other k-space sampling patterns used by MRI systems. These include “radial”, or “projection reconstruction” scans in which k-space is sampled as a set of radial sampling trajectories extending from the center of k-space. There are also many k-space sampling methods that are closely related to the radial scan and that sample along a curved k-space sampling trajectory rather than the straight line radial trajectory.
Depending on the technique used, many MR scans currently require many minutes to acquire the necessary data used to produce medical images. The reduction of this scan time is an important consideration, since reduced scan time increases patient throughout, improves patient comfort, and improves image quality by reducing motion artifacts. Many different strategies have been developed to shorten the scan time.
One such strategy is referred to generally as “parallel MRI” (“pMRI”). Parallel MRI techniques use spatial information from arrays of radio frequency (“RF”) receiver coils to substitute for the spatial encoding that would otherwise have to be obtained in a sequential fashion using RF pulses and magnetic field gradients, such as phase and frequency encoding gradients. Each of the spatially independent receiver coils of the array carries certain spatial information and has a different spatial sensitivity profile. This information is utilized in order to achieve a complete spatial encoding of the received MR signals, for example, by combining the simultaneously acquired data received from each of the separate coils.
The combination of the separate MR signals produced by the separate receiver coils enables a reduction of the acquisition time required for an image, in comparison to a conventional k-space data acquisition, by a factor related to the number of the receiver coils. Thus the use of multiple receiver coils acts to multiply imaging speed, without increasing gradient switching rates or RF power.
Two categories of parallel imaging techniques that have been developed and applied to in vivo imaging are so-called “image space methods” and “k-space methods.” An example image space method is known in the art as sensitivity encoding (“SENSE”), while an example k-space method is known in the art as simultaneous acquisition of spatial harmonics (“SMASH”). With SENSE, the undersampled k-space data are first Fourier transformed to produce an aliased image from each coil, and then the aliased image signals are unfolded by a linear transformation of the superimposed pixel values. With SMASH, the omitted k-space lines are synthesized or reconstructed prior to Fourier transformation, by constructing a weighted combination of neighboring k-space lines acquired by the different receiver coils. SMASH requires that the spatial sensitivity of the coils be determined, and one way to do so is by “autocalibration” that entails the use of variable density k-space sampling.
A more recent advance to SMASH techniques using autocalibration is a technique known as generalized autocalibrating partially parallel acquisitions (“GRAPPA”), as described, for example, in U.S. Pat. No. 6,841,998. With GRAPPA, k-space lines near the center of k-space are sampled at the Nyquist frequency, in comparison to the undersampling employed in the peripheral regions of k-space. These center k-space lines are referred to as the so-called autocalibration signal (“ACS”) lines, which are used to determine the weighting factors that are utilized to synthesize, or reconstruct, the missing k-space lines. In particular, a linear combination of individual coil data is used to create the missing lines of k-space. The coefficients for the combination are determined by fitting the acquired data to the more highly sampled data near the center of k-space.
Reconstructing non-Cartesian parallel imaging scans by synthesizing unacquired k-space data from neighboring acquired data remains a computationally burdensome endeavor. It would therefore be desirable to provide a system and method capable of synthesizing k-space data from non-Cartesian acquisitions.